Pith Number

pith:OAAROTXH

pith:2026:OAAROTXH7PCR3ZVR2VRIXDPYHP

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Equilibrium and Pricing in Consumer Networks with Nonlinear Utilities: An Online Shape-Constrained Learning Approach

Daniele Bracale, George Michailidis

Consumer networks with nonlinear utilities admit a unique equilibrium that enables targeted monopoly pricing and online recovery of unknown demand functions.

arxiv:2605.14193 v1 · 2026-05-13 · math.ST · stat.TH

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Claims

C1strongest claim

We establish the existence and uniqueness of the consumer-side equilibrium under general contraction and variational conditions, explicitly accommodating asymmetric and signed network externalities... we establish strict no-regret convergence guarantees.

C2weakest assumption

Consumer utilities satisfy contraction and variational conditions that guarantee a unique equilibrium; the abstract provides no explicit verification that these hold for the listed nonlinear families beyond the linear-quadratic case.

C3one line summary

The paper establishes equilibrium existence and uniqueness for nonlinear utility consumer networks under contraction conditions and proposes a shape-constrained isotonic regression approach with strict no-regret convergence for learning utilities in targeted monopoly pricing.

References

136 extracted · 136 resolved · 2 Pith anchors

[1] Journal of econometrics , volume= 1985

[2] Journal of econometrics , volume= 1975

[3] Journal of labor economics , volume= 1983

[4] International Conference on Artificial Intelligence and Statistics , pages= 2022

[5] 44th Annual IEEE Symposium on Foundations of Computer Science, 2003 2003

Receipt and verification

First computed	2026-05-17T23:39:11.121213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7001174ee7fbc51de6b1d5628b8df83bdbec14ac334757233aea387259fa9995

Aliases

arxiv: 2605.14193 · arxiv_version: 2605.14193v1 · doi: 10.48550/arxiv.2605.14193 · pith_short_12: OAAROTXH7PCR · pith_short_16: OAAROTXH7PCR3ZVR · pith_short_8: OAAROTXH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OAAROTXH7PCR3ZVR2VRIXDPYHP \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7001174ee7fbc51de6b1d5628b8df83bdbec14ac334757233aea387259fa9995

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ae540d71354ac1ef278973177e1406e8d099e17f173fb3848036235c005d811",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-13T23:19:05Z",
    "title_canon_sha256": "da41530d64ec912165efa1f34473f8a6b4019da545feb27007c0ce19b104c483"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14193",
    "kind": "arxiv",
    "version": 1
  }
}